1. Statement of the Technical Field
The inventive arrangements relate generally to methods and apparatus for providing increased design flexibility for RF circuits, and more particularly to variable quarter-wave transformers.
2. Description of the Related Art
A quarter-wave transformer is a specialized transmission line that typically is used in radio frequency (RF) circuits to impedance match various circuit components. Notably, quarter-wave transformers can be incorporated into many types of RF circuit components. For example, quarter-wave transformers can be included as elements in multi-section transformers, directional couplers, power splitters, filters, resonant lines, etc. Quarter-wave transformers are commonly implemented on specially designed printed circuit boards or substrates and comprise a quarter-wave element, which is a transmission line section, one or more input ports, and one or more output ports.
As the name implies, the electrical length of the quarter-wave element is usually one-quarter of a wavelength of a selected frequency, but a quarter-wave transformer also can be any odd multiple (2n+1) of the one-quarter wavelength. Further, the proper characteristic impedance of a quarter-wave transformer is given by the formula Z0=√{square root over (Z1Z2)}, where Z0 is the desired characteristic impedance of the quarter-wave transformer, Z1 is the impedance of a first transmission line to be matched, and Z2 is the impedance of a second transmission line or load being matched to the first transmission line. When more than one transmission line is connected to the input port or output port of the quarter-wave transformer, for example as in a power divider, Z1 and Z2 are net impedance values.
Quarter-wave transformers can be formed in many different ways. One configuration, known as microstrip, places the quarter-wave transformer on a board surface and provides a second conductive layer, commonly referred to as a ground plane. A second type of configuration known as buried microstrip is similar except that the quarter-wave transformer is covered with a dielectric substrate material. In a third configuration, known as stripline, the quarter-wave transformer is sandwiched within substrate between two electrically conductive (ground) planes.
Two critical factors affecting the performance of a substrate material are permittivity (sometimes called the relative permittivity or εr) and permeability (sometimes referred to as relative permeability or μr). The relative permittivity and permeability determine the propagation velocity of a signal, which is approximately inversely proportional to √{square root over (με)}, and therefore effect the electrical length of a quarter-wave transformer. Further, ignoring loss, the characteristic impedance of a quarter-wave transformer, such as stripline or microstrip, is equal to √{square root over (L1/C1)} where Ll is the inductance per unit length and Cl is the capacitance per unit length. The values of Ll and Cl are generally determined by the permittivity and the permeability of the dielectric material(s) used to separate the transmission line structures as well as the physical geometry and spacing of the line structures.
In a conventional RF design, a substrate material is selected that has a relative permittivity value suitable for the design. Notably, conventional substrate materials typically have a relative permeability of approximately 1.0. Once the substrate material is selected, the quarter-wave transformer characteristic impedance and frequency optimization is exclusively adjusted by controlling the line geometry and physical structure. One problem encountered when designing such quarter-wave transformers is that quarter-wave transformers are generally optimized only for use at a single frequency and odd harmonics of that frequency. Hence, a circuit that includes a quarter-wave transformer typically does not perform well over a range of frequencies that are not harmonically related. Modern RF circuits, however, commonly process multiple signals operating on different frequencies. Accordingly, the use of conventional dielectric substrate arrangements have proven to be a limitation in designing quarter-wave transformers for modern RF circuits.